A child’s world is fresh and new and beautiful, full of wonder and excitement. It is our misfortune that for most of us that clear-eyed vision, that true instinct for what is beautiful and awe-inspiring, is dimmed and even lost before we reach adulthood.

A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible,—that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision.

A vision of the whole of life!. Could any human undertaking be ... more grandiose? This attempt stands without rival as the most audacious enterprise in which the mind of man has ever engaged ... Here is man, surrounded by the vastness of a universe in which he is only a tiny and perhaps insignificant part—and he wants to understand it.

All appearances to the contrary, the only watchmaker in nature is the blind forces of physics, albeit deployed in very special way. A true watchmaker has foresight: he designs his cogs springs, and plans their interconnections, with a future purpose in his mind's eye. Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind's eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker.

All these delusions of Divination have their root and foundation from Astrology. For whether the lineaments of the body, countenance, or hand be inspected, whether dream or vision be seen, whether marking of entrails or mad inspiration be consulted, there must be a Celestial Figure first erected, by the means of whole indications, together with the conjectures of Signs and Similitudes, they endeavour to find out the truth of what is desired.

Although the ocean’s surface seems at first to be completely homogeneous, after half a month we began to differentiate various seas and even different parts of oceans by their characteristic shades. We were astonished to discover that, during an flight, you have to learn anew not only to look, but also to see. At first the finest nuances of color elude you, but gradually your vision sharpens and your color perception becomes richer, and the planet spreads out before you with all its indescribable beauty.

And science, we should insist, better than other discipline, can hold up to its students and followers an ideal of patient devotion to the search to objective truth, with vision unclouded by personal or political motive, not tolerating any lapse from precision or neglect of any anomaly, fearing only prejudice and preconception, accepting nature’s answers humbly and with courage, and giving them to the world with an unflinching fidelity. The world cannot afford to lose such a contribution to the moral framework of its civilisation.

As an adolescent I aspired to lasting fame, I craved factual certainty, and I thirsted for a meaningful vision of human life—so I became a scientist. This is like becoming an archbishop so you can meet girls.

As he [Clifford] spoke he appeared not to be working out a question, but simply telling what he saw. Without any diagram or symbolic aid he described the geometrical conditions on which the solution depended, and they seemed to stand out visibly in space. There were no longer consequences to be deduced, but real and evident facts which only required to be seen. … So whole and complete was his vision that for the time the only strange thing was that anybody should fail to see it in the same way. When one endeavored to call it up again, and not till then, it became clear that the magic of genius had been at work, and that the common sight had been raised to that higher perception by the power that makes and transforms ideas, the conquering and masterful quality of the human mind which Goethe called in one word das Dämonische.

As historians, we refuse to allow ourselves these vain speculations which turn on possibilities that, in order to be reduced to actuality, suppose an overturning of the Universe, in which our globe, like a speck of abandoned matter, escapes our vision and is no longer an object worthy of our regard. In order to fix our vision, it is necessary to take it such as it is, to observe well all parts of it, and by indications infer from the present to the past.

Ask a follower of Bacon what [science] the new philosophy, as it was called in the time of Charles the Second, has effected for mankind, and his answer is ready; “It has lengthened life; it has mitigated pain; it has extinguished diseases; it has increased the fertility of the soil; it has given new securities to the mariner; it has furnished new arms to the warrior; it has spanned great rivers and estuaries with bridges of form unknown to our fathers; it has guided the thunderbolt innocuously from heaven to earth; it has lighted up the night with the splendour of the day; it has extended the range of the human vision; it has multiplied the power of the human muscles; it has accelerated motion; it has annihilated distance; it has facilitated intercourse, correspondence, all friendly offices, all dispatch of business; it has enabled man to descend to the depths of the sea, to soar into the air, to penetrate securely into the noxious recesses of the earth, to traverse the land in cars which whirl along without horses, to cross the ocean in ships which run ten knots an hour against the wind. These are but a part of its fruits, and of its first-fruits; for it is a philosophy which never rests, which has never attained, which is never perfect. Its law is progress. A point which yesterday was invisible is its goal to-day, and will be its starting-point to-morrow.”

Be daring, be different, be impractical; be anything that will assert integrity of purpose and imagination vision against the play-it-safers, the creatures of the commonplace, the slave of the ordinary.

Before Kuhn, most scientists followed the place-a-stone-in-the-bright-temple-of-knowledge tradition, and would have told you that they hoped, above all, to lay many of the bricks, perhaps even the keystone, of truth’s temple. Now most scientists of vision hope to foment revolution. We are, therefore, awash in revolutions, most self-proclaimed.

Before the promulgation of the periodic law the chemical elements were mere fragmentary incidental facts in nature; there was no special reason to expect the discovery of new elements, and the new ones which were discovered from time to time appeared to be possessed of quite novel properties. The law of periodicity first enabled us to perceive undiscovered elements at a distance which formerly were inaccessible to chemical vision, and long ere they were discovered new elements appeared before our eyes possessed of a number of well-defined properties.

In Faraday Lecture, delivered before the Fellows of the Chemical Society in the Theatre of the Royal Institution (4 Jun 1889), printed in Professor Mendeléeff, 'The Periodic Law of the Chemical Elements', Transactions of the Chemical Society (1889), 55, 648.

Believing, as I do, in the continuity of nature, I cannot stop abruptly where our microscopes cease to be of use. Here the vision of the mind authoritatively supplements the vision of the eye. By a necessity engendered and justified by science I cross the boundary of the experimental evidence, and discern in that Matter which we, in our ignorance of its latent powers, and notwithstanding our professed reverence for its Creator, have hitherto covered with opprobrium, the promise and potency of all terrestrial Life.

'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 191.

Beyond these are other suns, giving light and life to systems, not a thousand, or two thousand merely, but multiplied without end, and ranged all around us, at immense distances from each other, attended by ten thousand times ten thousand worlds, all in rapid motion; yet calm, regular and harmonious—all space seems to be illuminated, and every particle of light a world. ... all this vast assemblages of suns and worlds may bear no greater proportion to what lies beyond the utmost boundaries of human vision, than a drop of water to the ocean.

But concerning vision alone is a separate science formed among philosophers, namely, optics, and not concerning any other sense ... It is possible that some other science may be more useful, but no other science has so much sweetness and beauty of utility. Therefore it is the flower of the whole of philosophy and through it, and not without it, can the other sciences be known.

Champions aren’t made in gyms. Champions are made from something they have deep inside them—a desire, a dream, a vision. They have to have last-minute stamina, they have to be a little faster, they have to have the skill and the will. But the will must be stronger than the skill.

Told to his Harvard students. As quoted, without citation, by Marcus Bach, 'Serendiptiy in the Business World', in The Rotarian (Oct 1981), 139, No. 4, 40. If you know a primary source, please contact Webmaster.

Despite the vision and the far-seeing wisdom of our wartime heads of state, the physicists felt a peculiarly intimate responsibility for suggesting, for supporting, and in the end, in large measure, for achieving the realization of atomic weapons. Nor can we forget that these weapons, as they were in fact used, dramatized so mercilessly the inhumanity and evil of modern war. In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.

Euclid alone has looked on Beauty bare.Let all who prate of Beauty hold their peace,And lay them prone upon the earth and ceaseTo ponder on themselves, the while they stareAt nothing, intricately drawn nowhereIn shapes of shifting lineage; let geeseGabble and hiss, but heroes seek releaseFrom dusty bondage into luminous air.O blinding hour, O holy, terrible day,When first the shaft into his vision shoneOf light anatomized! Euclid aloneHas looked on Beauty bare. Fortunate theyWho, though once only and then but far away,Have heard her massive sandal set on stone.

His reaction to a harsh, inaccurate, article in the New York Times that questioned the practicality of his goals in rocket research, (1920). As quoted by Dr. Kurt Debus, Director of Kennedy Space Center, NASA, in address (15 Jul 1965) at First World Exhibition of Transport and communications, Munich, collected in Chronology on Astronautics and Aeronautics in 1965 (1966), 332. This is the earliest evidence of this quote that Webmaster, as yet, has found. Please contact Webmaster if you know the primary source.

Experience hobbles progress and leads to abandonment of difficult problems; it encourages the initiated to walk on the shady side of the street in the direction of experiences that have been pleasant. Youth without experience attacks the unsolved problems which maturer age with experience avoids, and from the labors of youth comes progress. Youth has dreams and visions, and will not be denied.

Facts are not pure unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural.

Five per cent vision is better than no vision at all. Five per cent hearing is better than no hearing at all. Five per cent flight efficiency is better than no flight at all. It is thoroughly believable that every organ or apparatus that we actually see is the product of a smooth trajectory through animal space, a trajectory in which every intermediate stage assisted survival and reproduction.[Rebutting the Creationist assertion that fully developed organs could not have arisen 'by chance.']

For most scientists, I think the justification of their work is to be found in the pure joy of its creativeness; the spirit which moves them is closely akin to the imaginative vision which inspires an artist.

Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.

Genetics has enticed a great many explorers during the past two decades. They have labored with fruit-flies and guinea-pigs, with sweet peas and corn, with thousands of animals and plants in fact, and they have made heredity no longer a mystery but an exact science to be ranked close behind physics and chemistry in definiteness of conception. One is inclined to believe, however, that the unique magnetic attraction of genetics lies in the vision of potential good which it holds for mankind rather than a circumscribed interest in the hereditary mechanisms of the lowly species used as laboratory material. If man had been found to be sharply demarcated from the rest of the occupants of the world, so that his heritage of physical form, of physiological function, and of mental attributes came about in a superior manner setting him apart as lord of creation, interest in the genetics of the humbler organisms—if one admits the truth—would have flagged severely. Biologists would have turned their attention largely to the ways of human heredity, in spite of the fact that the difficulties encountered would have rendered progress slow and uncertain. Since this was not the case, since the laws ruling the inheritance of the denizens of the garden and the inmates of the stable were found to be applicable to prince and potentate as well, one could shut himself up in his laboratory and labor to his heart's content, feeling certain that any truth which it fell to his lot to discover had a real human interest, after all.

Good scholars struggle to understand the world in an integral way (pedants bite off tiny bits and worry them to death). These visions of reality ... demand our respect, for they are an intellectual’s only birthright. They are often entirely wrong and always flawed in serious ways, but they must be understood honorably and not subjected to mayhem by the excision of patches.

Great thinkers build their edifices with subtle consistency. We do our intellectual forebears an enormous disservice when we dismember their visions and scan their systems in order to extract a few disembodied ‘gems’–thoughts or claims still accepted as true. These disarticulated pieces then become the entire legacy of our ancestors, and we lose the beauty and coherence of older systems that might enlighten us by their unfamiliarity–and their consequent challenge in our fallible (and complacent) modern world.

Hyper-selectionism has been with us for a long time in various guises; for it represents the late nineteenth century’s scientific version of the myth of natural harmony–all is for the best in the best of all possible worlds (all structures well designed for a definite purpose in this case). It is, indeed, the vision of foolish Dr. Pangloss, so vividly satirized by Voltaire in Candide–the world is not necessarily good, but it is the best we could possibly have.

I believe television is going to be the test of the modern world, and that in this new opportunity to see beyond the range of our vision we shall discover either a new and unbearable disturbance of the general peace or a saving radiance in the sky. We shall stand or fall by television—of that I am quite sure

I have therefore tried to show the tendency displayed throughout history, by the most profound investigators, to pass from the world of the senses to a world where vision becomes spiritual, where principles are elaborated, and from which the explorer emerges with conceptions and conclusions, to be approved or rejected according as they coincide with sensible things.

I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at first their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.

I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.

If the Humours of the Eye by old Age decay, so as by shrinking to make the Cornea and Coat of the Crystalline Humour grow flatter than before, the Light will not be refracted enough, and for want of a sufficient Refraction will not converge to the bottom of the Eye but to some place beyond it, and by consequence paint in the bottom of the Eye a confused Picture, and according to the Indistinctuess of this Picture the Object will appear confused. This is the reason of the decay of sight in old Men, and shews why their Sight is mended by Spectacles. For those Convex glasses supply the defect of plumpness in the Eye, and by increasing the Refraction make the rays converge sooner, so as to convene distinctly at the bottom of the Eye if the Glass have a due degree of convexity. And the contrary happens in short-sighted Men whose Eyes are too plump. For the Refraction being now too great, the Rays converge and convene in the Eyes before they come at the bottom; and therefore the Picture made in the bottom and the Vision caused thereby will not be distinct, unless the Object be brought so near the Eye as that the place where the converging Rays convene may be removed to the bottom, or that the plumpness of the Eye be taken off and the Refractions diminished by a Concave-glass of a due degree of Concavity, or lastly that by Age the Eye grow flatter till it come to a due Figure: For short-sighted Men see remote Objects best in Old Age, and therefore they are accounted to have the most lasting Eyes.

In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.

In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur yet their cosmic quest destroyed the medieval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.

In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur … yet their cosmic quest destroyed the mediaeval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.

It is only by introducing the young to great literature, drama and music, and to the excitement of great science that we open to them the possibilities that lie within the human spirit—enable them to see visions and dream dreams.

Quoted, without citation in Reader's Digest Quotable Quotes (1997), 144. This quote, usually seen attributed as 'Eric Anderson' is here tentatively linked to Sir Eric Anderson. If you can confirm this with a primary source, please contact Webmaster.

It must be admitted that science has its castes. The man whose chief apparatus is the differential equation looks down upon one who uses a galvanometer, and he in turn upon those who putter about with sticky and smelly things in test tubes. But all of these, and most biologists too, join together in their contempt for the pariah who, not through a glass darkly, but with keen unaided vision, observes the massing of a thundercloud on the horizon, the petal as it unfolds, or the swarming of a hive of bees. And yet sometimes I think that our laboratories are but little earthworks which men build about themselves, and whose puny tops too often conceal from view the Olympian heights; that we who work in these laboratories are but skilled artisans compared with the man who is able to observe, and to draw accurate deductions from the world about him.

It was to Hofmeister, working as a young man, an amateur and enthusiast, in the early morning hours of summer months, before business, at Leipzig in the years before 1851, that the vision first appeared of a common type of Life-Cycle, running through Mosses and Ferns to Gymnosperms and Flowering Plants, linking the whole series in one scheme of reproduction and life-history.

It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.

Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?

Mankind have been slow to believe that order reigns in the universe—that the world is a cosmos and a chaos.… The divinities of heathen superstition still linger in one form or another in the faith of the ignorant, and even intelligent men shrink from the contemplation of one supreme will acting regularly, not fortuitously, through laws beautiful and simple rather than through a fitful and capricious system of intervention.... The scientific spirit has cast out the demons, and presented us with nature clothed in her right mind and living under the reign of law. It has given us, for the sorceries of the alchemist, the beautiful laws of chemistry; for the dreams of the astrologer, the sublime truths of astronomy; for the wild visions of cosmogony, the monumental records of geology; for the anarchy of diabolism, the laws of God.

Speech (16 Dec 1867) given while a member of the U.S. House of Representatives, introducing resolution for the appointment of a committee to examine the necessities for legislation upon the subject of the ninth census to be taken the following year. Quoted in John Clark Ridpath, The Life and Work of James A. Garfield (1881), 216.

Mars tugs at the human imagination like no other planet. With a force mightier than gravity, it attracts the eye to its shimmering red presence in the clear night sky. It is like a glowing ember in a field of ethereal lights, projecting energy and promise. It inspires visions of an approachable world. The mind vaults to thoughts of what might have been (if Mars were a litter closer to the warming Sun) and of what could be (if humans were one day to plant colonies there). Mysterious Mars, alluring Mars, fourth planet from the Sun: so far away and yet, on a cosmic scale, so very near.

Nature is objective, and nature is knowable, but we can only view her through a glass darkly–and many clouds upon our vision are of our own making: social and cultural biases, psychological preferences, and mental limitations (in universal modes of thought, not just individualized stupidity).

New frontiers of the mind are before us, and if they are pioneered with the same vision, boldness, and drive with which we have waged this war we can create a fuller and more fruitful employment and a fuller and more fruitful life.

No other part of science has contributed as much to the liberation of the human spirit as the Second Law of Thermodynamics. Yet, at the same time, few other parts of science are held to be so recondite. Mention of the Second Law raises visions of lumbering steam engines, intricate mathematics, and infinitely incomprehensible entropy. Not many would pass C.P. Snow’s test of general literacy, in which not knowing the Second Law is equivalent to not having read a work of Shakespeare.

Nothing is more humbling than to look with a strong magnifying glass at an insect so tiny that the naked eye sees only the barest speck and to discover that nevertheless it is sculpted and articulated and striped with the same care and imagination as a zebra. Apparently it does not occur to nature whether or not a creature is within our range of vision, and the suspicion arises that even the zebra was not designed for our benefit.

Our revels are now ended. These our actors,As I foretold you, were all spirits, and Are melted into air, into thin air;And like the baseless fabric of this vision,The cloud-capp'd towers, the gorgeous palaces,The solemn temples, the great globe itself,Yea, all which it inherit, shall dissolve.And like this insubstantial pageant faded,Leave not a rack behind. We are such stuffAs dreams are made on; and our little lifeIs rounded with a sleep.

Physicians get neither name nor fame by the pricking of wheals or the picking out thistles,
or by laying of plaisters to the scratch of a pin; every old woman can do this. But if they would have a name and a fame, if they will have it quickly, they must do some great and desperate cures. Let them fetch one to life that was dead; let them recover one to his wits that was mad; let them make one that was born blind to see; or let them give ripe wits to a fool: these are notable cures, and he that can do thus, if he doth thus first, he shall have the name and fame he deserves; he may lie abed till noon.

Richard Drew embodied the essential spirit of the inventor, a person of vision and unrelenting persistence who refused to give in to adversity. He made an enormous contribution, not only to the growth of 3M, but also to advancement of many modern industries vital to worldwide economic growth.

Science and poetry are, in fact, inseparable. By providing a vision of life, of Earth, of the universe in all its splendor, science does not challenge human values; it can inspire human values. It does not negate faith; it celebrates faith.

Science is not the enemy of humanity but one of the deepest expressions of the human desire to realize that vision of infinite knowledge. Science shows us that the visible world is neither matter nor spirit; the visible world is the invisible organization of energy.

Scientific observation has established that education is not what the teacher gives; education is a natural process spontaneously carried out by the human individual, and is acquired not by listening to words but by experiences upon the environment. The task of the teacher becomes that of preparing a series of motives of cultural activity, spread over a specially prepared environment, and then refraining from obtrusive interference. Human teachers can only help the great work that is being done, as servants help the master. Doing so, they will be witnesses to the unfolding of the human soul and to the rising of a New Man who will not be a victim of events, but will have the clarity of vision to direct and shape the future of human society.

Sir Mortimer Wheeler is perhaps the most distinguished archaeologist in Europe. But he owes the greatest of his achievements to the rare combination of two qualities: namely a scientific expertise in the technique of excavation which has always been marked by a meticulous attention to minute detail, and a gift of imaginative vision.

Such is the character of mathematics in its profounder depths and in its higher and remoter zones that it is well nigh impossible to convey to one who has not devoted years to its exploration a just impression of the scope and magnitude of the existing body of the science. An imagination formed by other disciplines and accustomed to the interests of another field may scarcely receive suddenly an apocalyptic vision of that infinite interior world. But how amazing and how edifying were such a revelation, if it only could be made.

Suddenly, there was an enormous flash of light, the brightest light I have ever seen or that I think anyone has ever seen. It blasted; it pounced; it bored its way into you. It was a vision which was
seen with more than the eye. It was seen to last forever. You would wish it would stop; altogether it lasted about two seconds.[Witnessing the first atomic bomb test explosion.]

The double horror of two Japanese city names [Hiroshima and Nagasaki] grew for me into another kind of double horror; an estranging awareness of what the United States was capable of, the country that five years before had given me its citizenship; a nauseating terror at the direction the natural sciences were going. Never far from an apocalyptic vision of the world, I saw the end of the essence of mankind an end brought nearer, or even made, possible, by the profession to which I belonged. In my view, all natural sciences were as one; and if one science could no longer plead innocence, none could.

The effort of the economist is to see, to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.

The Einsteinian and the Newtonian vision of the world are two faithful reflectors of it: just as the two images, polarized in opposite directions, which Iceland spar shows us in its strange crystal both share the light of the same object.

The engineer is the key figure in the material progress of the world. It is his engineering that makes a reality of the potential value of science by translating scientific knowledge into tools, resources, energy and labor to bring them to the service of man ... To make contribution of this kind the engineer requires the imagination to visualize the needs of society and to appreciate what is possible as well as the technological and broad social age understanding to bring his vision to reality.

The evening was calm, the calmest we had known above the North Col. The smooth, outward dipping slabs glowed in the fast setting sun and, at an immense distance beneath, clouds concealed the valleys and lesser peaks. There was nothing to obstruct the tremendous prospect. Seen from Everest, great peaks that dominate the climber as he toils along the East Rongbuk Glacier, and up the slopes of the North Col, show like insignificant ripples at the base of a great ocean roller. Even the North Peak was but a stepping-stone to quick-footed vision.

The great scientists have been occupied with values—it is only their vulgar followers who think they are not. If scientists like Descartes, Newton, Einstein, Darwin, and Freud don’t “look deeply into experience,” what do they do? They have imaginations as powerful as any poet’s and some of them were first-rate writers as well. How do you draw the line between Walden and The Voyage of the Beagle? The product of the scientific imagination is a new vision of relations—like that of the artistic imagination.

The history of Europe is the history of Rome curbing the Hebrew and the Greek, with their various impulses of religion, and of science, and of art, and of quest for material comfort, and of lust of domination, which are all at daggers drawn with each other. The vision of Rome is the vision of the unity of civilisation.

The history of mathematics is exhilarating, because it unfolds before us the vision of an endless series of victories of the human mind, victories without counterbalancing failures, that is, without dishonorable and humiliating ones, and without atrocities.

The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me—both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

The position of the anthropologist of to-day resembles in some sort the position of classical scholars at the revival of learning. To these men the rediscovery of ancient literature came like a revelation, disclosing to their wondering eyes a splendid vision of the antique world, such as the cloistered of the Middle Ages never dreamed of under the gloomy shadow of the minster and within the sound of its solemn bells. To us moderns a still wider vista is vouchsafed, a greater panorama is unrolled by the study which aims at bringing home to us the faith and the practice, the hopes and the ideals, not of two highly gifted races only, but of all mankind, and thus at enabling us to follow the long march, the slow and toilsome ascent, of humanity from savagery to civilization. And as the scholar of the Renaissance found not merely fresh food for thought but a new field of labour in the dusty and faded manuscripts of Greece and Rome, so in the mass of materials that is steadily pouring in from many sides—from buried cities of remotest antiquity as well as from the rudest savages of the desert and the jungle—we of to-day must recognise a new province of knowledge which will task the energies of generations of students to master.

The pursuit of science has often been compared to the scaling of mountains, high and not so high. But who amongst us can hope, even in imagination, to scale the Everest and reach its summit when the sky is blue and the air is still, and in the stillness of the air survey the entire Himalayan range in the dazzling white of the snow stretching to infinity? None of us can hope for a comparable vision of nature and of the universe around us. But there is nothing mean or lowly in standing in the valley below and awaiting the sun to rise over Kinchinjunga.

The regularity with which we conclude that further advances in a particular field are impossible seems equaled only by the regularity with which events prove that we are of too limited vision. And it always seems to be those who have the fullest opportunity to know who are the most limited in view. What, then, is the trouble? I think that one answer should be: we do not realize sufficiently that the unknown is absolutely infinite, and that new knowledge is always being produced.

The universe flows, carrying with it milky ways and worlds, Gondwanas and Eurasias, inconsistent visions and clumsy systems. But the good conceptual models, these serena templa of intelligence on which several masters have worked, never disappear entirely. They are the great legacy of the past. They linger under more and more harmonious forms and actually never cease to grow. They bring solace by the great art that is inseparable from them. Their permanence relies on the immortal poetry of truth, of the truth that is given to us in minute amounts, foretelling an order whose majesty dominates time.

There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is anybody’s guess. …

These days at ten o’clock at night a most alarming wonder has manifested itself in the skies. The firmament was rent asunder and through this gap one could distinguish chariots and armies, riders with yellow, white, red and black standards, though to do battle against each other. This awesome and unusual vision continued from ten at night till about two of the morning, and was witnessed with alarm and dismay by many honest and trustworthy people. The significance thereof is known but to God Almighty, Who may graciously prevent the shedding of innocent blood.

'Frightful Apparition in the Sky at Vienna. From Vienna, the 11th day of August 1590'. As quoted in George Tennyson Matthews (ed.) News and Rumor in Renaissance Europe: The Fugger Newsletters (1959), 188. A handwritten collection of news reports (1568-1604) by the powerful banking and merchant house of Fugger in Ausburg.

This is the questionMarryChildren—(if it Please God)—Constant companion (& friend in old age) who will feel interested in one—object to be beloved and played with—better than a dog anyhow. Home, & someone to take care of house—Charms of music and female chit-chat.—These things good for one’s health.—but terrible loss of time.—My God, it is Intolerable to think of spending ones whole life, like a neuter bee, working, working—& nothing after all.—No, no, won’t do. Imagine living all one’s day solitary in smoky dirty London House.—Only picture to yourself a nice soft wife on a sofa with good fire, & books & music perhaps-—Compare this vision with the dingy reality of Grt. Marlbro’ Street.Not MarryFreedom to go where one liked—choice of Society and little of it. —Conversation of clever men at clubs—Not forced to visit relatives, & to bend in every trifle. —to have the expense and anxiety of children—perhaps quarreling—Loss of time. —cannot read in the Evenings—fatness & idleness—Anxiety & responsibility—less money for books &c—if many children forced to gain one’s bread. —(but then it is very bad for ones health to work too much) Perhaps my wife won’t like London; then the sentence is banishment & degradation into indolent, idle fool.Marry—Marry—Marry Q.E.D.It being proved necessary to Marry When? Soon or late?

This very important property of rods, and indeed also of each kind of cone, this limitation of output to a single dimension of change, may be called the Principle of Univariance and stated thus: “The output of a receptor depends upon its quantum catch, but not upon what quanta are caught.” … Young's theory of colour vision may now be stated in terms of cone pigments. “There are three classes of cone each containing a different visual pigment. The output of each cone is univariant, depending simply upon the quantum catch of its pigment. Our sensation of colour depends upon the ratios of these three cone outputs.”

Principle of Univariance, concerning color vision, as stated in Lecture to a meeting of the Physiological Society at Chelsea College, London (17 Apr 1970), and reported in 'Pigments and Signals in Colour Vision', The Journal of Physiology (1972), 220 No. 3, 4P.

Time’s arrow of ‘just history’ marks each moment of time with a distinctive brand. But we cannot, in our quest to understand history, be satisfied only with a mark to recognize each moment and a guide to order events in temporal sequence. Uniqueness is the essence of history, but we also crave some underlying generality, some principles of order transcending the distinction of moments–lest we be driven mad by Borges’s vision of a new picture every two thousand pages in a book without end. We also need, in short, the immanence of time’s cycle.

Unless there exist peculiar institutions for the support of such inquirers, or unless the Government directly interfere, the contriver of a thaumatrope may derive profit from his ingenuity, whilst he who unravels the laws of light and vision, on which multitudes of phenomena depend, shall descend unrewarded to the tomb.

Vision, in my view, is the cause of the greatest benefit to us, inasmuch as none of the accounts now given concerning the Universe would ever have been given if men had not seen the stars or the sun or the heavens. But as it is, the vision of day and night and of months and circling years has created the art of number and has given us not only the notion of Time but also means of research into the nature of the Universe. From these we have procured Philosophy in all its range, than which no greater boon ever has come or will come, by divine bestowal, unto the race of mortals.

We have taken to the Moon the wealth of this nation,the vision of its political leaders,the intelligence of its scientists,the dedication of its engineers,the careful craftsmanship of its workers,and the enthusiastic support of its people.We have brought back rocks, and I think it is a fair trade . . .Man has always gone where he has been able to go. It’s that simple.He will continue pushing back his frontier,no matter how far it may carry him from his homeland.

We lift ourselves by our thought. We climb upon our vision of ourselves. If you want to enlarge your life, you must first enlarge your thought of it and of yourself. Hold the ideal of yourself as you long to be, always everywhere.

We need a new vision for agriculture … to spread happiness among farm and rural families. Bio-happiness through the conversion of our bio-resources into wealth meaningful to our rural families should be the goal of our national policy for farmers.

What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.

From Physics Survey Committee, U.S. National Academy of Sciences, National
Research Council, 'The Nature of Physics', in report Physics in Perspective (1973), 61-62. As cited in I. Bernard Cohen, Revolution in Science (1985), 554-555.

While speaking, M. Bertrand is always in motion; now he seems in combat with some outside enemy, now he outlines with a gesture of the hand the figures he studies. Plainly he sees and he is eager to paint, this is why he calls gesture to his aid. With M. Hermite, it is just the opposite; his eyes seem to shun contact with the world; it is not without, it is within he seeks the vision of truth.

Ye daring ones! Ye venturers and adventurers, and whoever of you have embarked with cunning sails on unexplored seas! Ye enjoyers of enigmas! Solve unto me the enigma that I then beheld, interpret for me the vision of the loneliest one. ... O my brethren, I heard a laughter which was no human laughter.

Years ago I used to worry about the degree to which I specialized. Vision is limited enough, yet I was not really working on vision, for I hardly made contact with visual sensations, except as signals, nor with the nervous pathways, nor the structure of the eye, except the retina. Actually my studies involved only the rods and cones of the retina, and in them only the visual pigments. A sadly limited peripheral business, fit for escapists. But it is as though this were a very narrow window through which at a distance, one can only see a crack of light. As one comes closer the view grows wider and wider, until finally looking through the same narrow window one is looking at the universe. It is like the pupil of the eye, an opening only two to three millimetres across in daylight, but yielding a wide angle of view, and manoeuvrable enough to be turned in all directions. I think this is always the way it goes in science, because science is all one. It hardly matters where one enters, provided one can come closer, and then one does not see less and less, but more and more, because one is not dealing with an opaque object, but with a window.

Your printers have made but one blunder,Correct it instanter, and then for the thunder!We’ll see in a jiffy if this Mr S[pencer]Has the ghost of a claim to be thought a good fencer.To my vision his merits have still seemed to dwindle,Since I have found him allied with the great Dr T[yndall]While I have, for my part, grown cockier and cockier,Since I found an ally in yourself, Mr L[ockyer]And am always, in consequence, thoroughly willin’,To perform in the pages of Nature's M[acmillan].

[Poincaré was] the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincare had, and none in his superior in the gift of clear exposition.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan